Gunjo Pachauri

Solution We haveNumber of faces F = 10Number of edges E = 20and number of vertices V = 15Euler’s formula:V + F – E = 2⇒ 15 + 10 – 20 = 2⇒ 5 ≠ 2Hence, it is not possible to have a polyhedron satisfying the above data

Solution Let us say, the two consecutive positive integers be x and x + 1.Therefore, as per the given statement,x² + (x + 1)² = 365⇒ x² + x² + 1 + 2x = 365⇒ 2x² + 2x – 364 = 0⇒ x² + x – 182 = 0⇒ x² + 14x – 13x –

Solution Given that the scale on the map is 1 mm: 6 mTo find the distance drawn on the map for an actual distance of 60 m,Scale of map = distance drawnActual distance1 = distance drawn6 60 mdistance drawn = 1 x 60 = 10 mm6Thus, the distance on the map for the actual distance

Solution Let us suppose Mohan rao will have to read x pages every day to finish the book in 8 days.As the number of days decreases, the number of pages increases.So, the number of days and number of pages are in inverse proportion.∴ 10 × 40 = 8 × xx=400/8⇒ x = 50 pagesHence, Mohan

Solution The AP can be expressed as a, (a + d), —, (a +10d).The sum of the first 3 terms is (3a + 3d) = 51 and that of the last 3 is (3a + 27d) = 99.Solving these equations, we get a = 15 and d = 2.The arithmetic mean of the 3 terms

Solution x²-45x+324=0Solving this quadratic equation-x²−36x−9x+324=0⇒x(x−36)−9(x−36)=0(x−9)(x−36)=0So, x = 9 and 36.

Solution Consider the equation 3x + 2y = 12Now, square both sides:(3x + 2y)² = 12²=> 9x² + 12xy + 4y² = 144=>9x² + 4y² = 144 – 12xyFrom the questions, xy = 6So,9x² + 4y² = 144 – 72Thus, the value of 9x² + 4y² = 72

Solution Let the number be x.Then the other number = x + 9Sum of two numbers = 45According to the question, x + (x + 9) = 45⇒ 2x + 9 = 45⇒ 2x = 45 – 9 (transposing 9 to the R.H.S changes to -9)⇒ 2x = 36⇒ 2x/2 = 36/2 (divide by 2

Solution Assume the natural number = xIf the number increased by 12 = x + 12Then,Reciprocal of the number = 1/xAs per the question, we get,x + 12 = 160 times of reciprocal for xx + 12 = 160/ xx( x + 12 ) = 160×2 + 12x – 160 = 0x2 + 20x –

Solution ∵ Thickness of one book = 20 mm∴ Thickness of 5 books = 5 × 20 mm = 100 mm Again,Thickness of 1 paper sheet = 0.016 mm∴ Thickness of 5 paper sheets = 5 × 0.016 mm= 0.080m∴ Total thickness = 100 mm + 0.080 mm= 100.08 mm = 1.0008 × 10² mm